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Benefit-Cost Analysis: Financial and Economic Appraisal Using
Spreadsheets
Book · June 2003
DOI: 10.1017/CBO9780511791291

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Richard P. C. Brown
The University of Queensland
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Benefit-Cost Analysis
Financial and Economic Appraisal using Spreadsheets

Harry F. Campbell and Richard P. C. Brown
The University of Queensland

Contents
List of figures
List of tables

vi
ix

Preface

xi

1

Benefit-Cost Analysis: Introduction and Overview

2

Investment Appraisal: Principles

18

3

Investment Appraisal: Decision-Rules

36

4

Private Benefit-Cost Analysis: Financial Analysis


62

5

Efficiency Benefit-Cost Analysis

92

6

Calculating the Net Benefits to the Referent Group

122

7

Consumer and Producer Surplus in Benefit-Cost Analysis

146

8

Valuing Traded and Non-traded Commodities in Benefit-Cost Analysis

177

9

Incorporating Risk in Benefit-Cost Analysis


194

10

The Social Discount Rate, Cost of Public Funds, and the Value of Information

221

11

Weighting Net Benefits to Account for Income Distribution

238

12

Valuation of Non-marketed Goods

261

13

Economic Impact Analysis

288

14

Writing the Benefit-Cost Analysis Report


304

Appendix 1: Case Study Assignment

332

Appendix 2: Discount and Annuity Tables

340

Index

1

342


Figures
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6

2.7
2.8
2.9
3.1
3.2
3.3
3.4
3.5
4.1
4.2
4.3
A4.1
A4.2
A4.3
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13

The “With and Without” Approach to Benefit-Cost Analysis
Typical Time-Stream of Project Net Benefits

Relationship between the Project, Private, Efficiency and
Referent Group Net Benefits
The Benefit-Cost Analysis Spreadsheet
Project Appraisal and Evaluation as a Continuous Process
Investment Appraisal – a Private Perspective
A Country’s Inter-temporal Production Possibilities Curve
The Inter-temporal Effects of International Trade
Net Benefit Stream of a Two-period Investment Project
Net Present Value in Relation to the Discount Rate
Calculating Internal Rates of Return – One Positive Value
Calculating Internal Rates of Return – Two Positive Values
Net Present Value in Relation to the Discount Rate – the Two Positive
Internal Rates of Return Case
Net Present Value in Relation to the Discount Rate – the No Internal
Rate of Return Case
Switching
Spreadsheet Presentation of DCF Calculation
Using Built-In Spreadsheet Formulae
Referencing within the Spreadsheet
Selecting and Pasting a Built-in Formula
NFG Case Study: Key Variables Table
NFG Case Study: Project Cash Flow Table
NFG Case Study: Private Net Benefits Table
ICP Project Solution: Key Input Variables
ICP Project Solution: The Project Cash Flow
ICP Project Solution: The Private Cash Flow
The Efficiency Benefit-Cost Analysis Pricing Rule
Competitive Market Equilibrium
The Effect of a Minimum Wage
An Individual’s Leisure Supply and Demand

The Market for Rental Units with Rent Control
The Market for an Imported Good Subject to a Tariff
The Market for Diesel Fuel Subject to a Subsidy
Demand and Costs in the Electricity Industry
Demand for Labour by a Monopoly
Supply for Labour to a Monopsony
Monopoly Output with and without a Subsidy
A Consumer Good Subject to an Indirect Tax
NFG Case Study: Key Variables Table with Efficiency Prices

3
5
7
12
15
19
22
23
25
26
27
28
29
30
48
54
56
58
59
80

81
83
89
89
90
93
94
97
99
100
101
102
103
105
106
107
109
115


Figures

5.14
A5.1
6.1
6.2
6.3
A6.1
A6.2
7.1

7.2(a)
7.2(b)
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
A7.1
8.1
8.2
8.3
8.4
8.5
9.1
9.2
9.3
9.4
9.5
9.6(a)
9.6(b)
9.6(c)
9.6(d)
9.6(e)
9.6(f)
9.6(g)

9.6(h)
9.6(i)
9.7

NFG Case Study: Efficiency Cash Flow Table
ICP Project Solution: The Efficiency Cash Flow
The Relationship between Referent Group and Non-referent Group
Net Benefits at Market Prices and Efficiency Prices
NFG Case Study: Referent Group Analysis Table
Distribution of Efficiency Net Benefits ($ thousands, @ 10% discount rate)
ICP Project Solution: The Referent Group Cash Flow
ICP Project Solution: Consolidated Tables
Consumer Surplus
Consumer Surplus with Inelastic Demand
Consumer Surplus with Elastic Demand
Benefits of a Bridge
Effect of a Bridge Toll
Subsidizing Bus Fares
Effects of Worker Training
Benefits of an Irrigation Project
Change in the Rental Value of Land
Irrigation Water Sold at Less than Market Value
Effect of an Increase in Demand for Labour
Effects of Building a Bridge on the Benefits from a Ferry
ICP Project Solution: Higher Skilled Wages
Compensating and Equivalent Variation
Consumption Opportunities with and without an Import-Replacing Project
The UNIDO and LM Approaches to Project Appraisal
The Foreign Exchange Market with a Fixed Exchange Rate
Supply and Demand for Foreign Exchange with Tariffs and Subsidies

ICP Project Solution with a Shadow Exchange Rate
Triangular Probability Distribution
Cumulative Probability Distribution
Projects with Different Degrees of Risk
The Relationship between Utility and Wealth for a Risk Averse Individual
A Risk Averse Individual’s Indifference Map between Mean and
Variance of Wealth
Entering the Data
Entering the Simulation Settings
Running the Simulation
Reading the Results of the Simulation
Graphing the Probability Distribution
Generating a Cumulative Probability Distribution
Saving the Risk Analysis Results to a Spreadsheet
Selecting a Range of Values as Risk Analysis Outputs
Producing Summary Graphs for a Range of Outputs
ICP Project Risk Analysis: Programming a “Random Walk”

vii

116
118
123
136
137
139
142
148
150
151

153
155
156
159
161
163
165
166
168
170
173
180
186
188
189
192
202
203
204
205
207
209
210
211
211
212
212
213
213
214

217


viii

9.8
9.9
10.1
10.2
10.3
11.1
11.2
11.3
11.4
12.1
12.2
12.3
12.4
12.5
12.6
13.1

Figures

ICP Project Risk Analysis: Summary Statistics for Referent Group Net Benefits
ICP Project Risk Analysis: Summary Graph for a Range of Discount Rates
Taxation and Labour Supply
The Benefit and Cost of Delaying an Investment
ICP Project Solution with a Premium on Public Funds
The Lorenz Curve

Total Utility Curve
Marginal Utility Curve
Weighting Factors for Extra Income
Total Economic Value of Coral Reef Ecosystems
Measures of Value using the Replacement Cost Method
Willingness-to-pay and Consumer Surplus
Change in Consumer Surplus from Demand Curve Shift
Change in Consumer Surplus Resulting from a Price Change
Approximate Individual Demand Curve for Park Visits
The Circular Flow of Income

218
218
228
231
235
240
245
246
249
267
272
274
275
275
277
289


Tables

3.1
3.2
3.3
3.4
3.5
3.6
4.1
4.2
4.3
4.4
4.5
4.6
4.7
A4.1
A4.2
A4.3
5.1
6.1
6.2
9.1
9.2
9.3
9.4
9.5
11.1
11.2
11.3
11.4
11.5
11.6

11.7
11.8
11.9
11.10
11.11
11.12
12.1
12.2
12.3

Discount Factors for 10% and 15% Discount Rates
Discounted Net Cash Flow for a Hypothetical Project ($ millions)
Ranking of Projects by NPV and Profitability Ratio ($ thousands)
Ranking Lumpy Projects ($ thousands)
Two Investments with Different Lives
Establishing Equal Project Lives
Nominal vs. Real Cash Flows
Incremental Cash Flows
Calculating Depreciation Using the Straight-Line Method
Investment in Working Capital
Deriving the Private Cash Flow on Farmer’s Equity
Project Cash Flows Equal Debt Plus Equity (Private) Cash Flows
NFG’s Annual Operating Costs
Investment Costs: Yarn-Spinning Project: ICP
Employment: Yarn-Spinning Project: ICP
Additional Cost of Locating in Southern Thailand
Indirect Taxes or Subsidies on NFG Project Inputs
Classification of Net Benefits
Using Shadow-prices to Identify Referent Group Benefits and Costs
Sensitivity Analysis Results: NPVs for Hypothetical Road Project

($ thousands at 10% discount rate)
A Discrete Probability Distribution of Road Construction Costs ($ thousands)
Calculating the Expected Value from a Discrete Probability Distribution
($ thousands)
Joint Probability Distribution: Correlated Variables ($ thousands)
Joint Probability Distribution: Uncorrelated Variables ($ thousands)
Distribution of Households by Annual Income
Income Distribution by Deciles
Distribution of Income by Sector
Income Distribution by Percentile
Comparing Projects with Different Atemporal Distributions
Comparing Projects with Different Aggregate Benefits and Distributions
Applying Distributional Weights to Project Net Benefits
Responsiveness of Distributional Weights to Changes in n
Threshold Distributional Weights
Distributional Weighting in the NFG Project
Threshold Combinations of Distributional Weights
Composite Distributional Weights
Hypothetical Water Quality Improvement Project Options
Hypothetical Travel Cost Example
Impact of Road Noise Changes on Property Values

39
39
50
51
52
52
65
68

70
71
73
74
79
86
87
88
114
123
126
197
198
199
200
200
239
239
240
241
243
244
244
249
253
254
255
258
270
277

280


x

Tables

12.4
12.5
13.1
A14.1
A14.2
A14.3
A14.4
A14.5
A14.6
A14.7
A14.8
A14.9
A14.10
A14.11
A14.12
A14.13

Estimating Net Benefits of Improved Water Quality using CVM
Example of a Hypothetical Choice Set
Inter-Industry Structure of a Small Closed Economy
Project Analysis
Private Analysis
Efficiency Analysis

Referent Group Analysis
Summary Information
Option 1: Bangkok – No Concessions – Key Variables
Option 1: Bangkok – No Concessions
Option 2: Bangkok – No Duties
Option 3: Bangkok – No Profits Tax
Option 4: Southern Thailand – No Concessions
Option 5: Southern Thailand – No Duties
Option 6: Southern Thailand – No Profits Tax
Option 7: Southern Thailand – No Duties, No Profits Tax

281
282
297
312
313
314
314
316
317
318
320
322
324
326
328
330


Preface

This book is intended for people with a basic understanding of elementary economics who
wish to learn how to conduct a social cost-benefit analysis. We use the term social benefit-cost
analysis to refer to the appraisal of a private or public project from a public interest viewpoint.
We follow professional practice in using the terms benefit-cost analysis and cost-benefit analysis
(with or without the social prefix) interchangeably.
A social cost-benefit analysis of a publicly funded project may be commissioned by a
municipal, state or federal government, or by an international agency such as the World Bank,
IMF, UN or OECD. Proponents of private projects which have significant social impacts may
also commission an economic analysis of this type in order to support an application for
approval to proceed with the project. Sometimes the scope of the required analysis is broader
than the evaluation of economic benefits and costs: an impact analysis may also be required to
determine the effects of the project on employment and economic growth; an environmental
impact statement may be required; and a social impact analysis dealing with factors such as
crime and impacts on families may be sought. This book concerns itself mainly with the
economic benefits and costs of projects, although it does touch on the question of economic
impact. The main questions addressed are: Do the benefits of the project exceed the costs, no
matter how widely they are spread? And which group benefits and which bears the costs?
Social cost-benefit analysis relies mainly on microeconomic theory, although some
understanding of macroeconomics is also useful. The person whose background should be sufficient to allow them to benefit from this book is someone who did a principles of economics
subject as part of a commerce, arts, science or engineering degree; a person with an undergraduate economics training will find the organizational principles set out in the book to be
innovative and of considerable practical use.
The book has several unique features: the close integration of spreadsheet analysis with
analytical principles is a feature of some financial appraisal texts, but is unusual in social
benefit-cost analysis; the particular layout of the spreadsheet is unique in offering an invaluable cross-check on the accuracy of the appraisal; and the book is structured in a way that
allows readers to choose the level of analysis which is relevant to their own purposes.
The book emphasizes practical application. It develops a template based on spreadsheet
analysis which is recommended for use in conducting a social cost-benefit analysis and which
provides a check on the accuracy of the analysis. The template is presented in the form of a case
study of a social cost-benefit analysis of a proposed private investment project in a developing
economy. The case study, together with reference to the necessary economic principles, is developed stage by stage in Part 1 of the book, consisting of the first six Chapters. At the completion

of Part 1 the reader should be capable of undertaking a cost-benefit analysis of an actual project.
Part 2 of the book introduces some complications which were ignored in Part 1: input or
output price changes caused by the project under analysis; imperfections in foreign exchange
markets; risk; and the cost of public funds. The analysis of many projects does not require consideration of these matters, and because they tend to be a little more complicated they are
deferred to this second Part of the book. The treatment of these issues in practical benefit-cost
analysis is illustrated by amendments to the case study developed in Part 1.


xii

Preface

Part 3 of the book looks at broader issues, including income distribution issues from an
atemporal and inter-temporal perspective, valuation of non-marketed goods, and economic
impact analysis.

Note to the Instructor
The book is intended as the required text for a sequence of two courses in benefit-cost analysis.
It provides a framework for courses involving practical application and leading to the acquisition of a valuable set of skills. It can be supplemented by a range of other readings chosen to
reflect the emphasis preferred by the Instructor. It includes exercises and a major benefit-cost
analysis problem which can be assigned for credit.
A one-semester undergraduate or postgraduate course can be based on Chapters 1–6 of
the book, or Chapters 1–7 if issues of consumer and producer surplus are to be included. We
suggest a weighting of 50% credit for examination of the principles put forward in the
Chapters, 10% for a selection from the small Exercises that follow each Chapter, and 40% for
completing the benefit-cost analysis assignment presented in the Appendix. Chapter 14,
dealing with the way in which a benefit-cost analysis should be reported, can also be assigned
as reading. The text can be supplemented with other reading, including reference to chapters
in other benefit-cost texts which cover some issues in more detail. Some classes might benefit
from a set of lectures on the basic microeconomic principles upon which benefit-cost analysis

draws, together with reference to a text in microeconomics or public finance.
A more advanced course can be built around Chapters 7–13 and selected parts of
Chapters 1–6, together with references to further reading. We teach the higher level course in
6–8 weeks in the second half of the semester, with completion of the basic course as a prerequisite. We use a weighting of 65% credit for examination of principles and 35% for
completion of the Exercises. However, a term paper on a particular issue in benefit-cost
analysis could be assigned for part of the credit.
For the purposes of the more advanced course the text needs to be supplemented by a
significant amount of further reading. In our course we recommend to our students some
chapters in some of the benefit-cost analyses texts referred to in our brief suggestions for
further reading, but the choice is very much a matter of individual taste.
Our teaching of the basic course is based on two hours of lectures and class discussion per
week plus a one-hour computer lab session. To start with we use the lab session to make sure
everyone is comfortable with using spreadsheets and is able to access the various financial subroutines. We then spend some time developing the benefit-cost analysis of the case study
project as an example of the practical application of the approach. After 6–7 weeks of lectures
and lab work students are ready to undertake the benefit-cost analysis assignment in the
Appendix. In the second part of the semester we use the class and lab times for consultations
with students who require help with the major assignment. As indicated by the sample case
study report, which was prepared by one of our students and is included in Chapter 14, a high
standard of work can be expected.


Preface

xiii

We use a similar teaching pattern for the more advanced course. The lab sessions are
used to provide help with the assignments, and consultation sessions can also be provided for
this purpose and for assistance with preparing a term paper. The benefit-cost analysis assignment in the Appendix could be expanded, as illustrated in the Appendices to Chapters 7–10,
and further development of the report prepared in the basic course could be the subject of a
significant assignment.

The text will be supported by a link on Cambridge University Press’ website
() which will provide the Instructor with access to spreadsheets, problem solutions and powerpoint presentations.

Acknowledgements
We have benefited greatly from teaching benefit-cost analysis over many years in several universities and we would like to thank our students, both past and present, for their contribution
to our understanding and presentation of the concepts which are the topic of this book. In particular we would like to thank Angela McIntosh for permission to include her case study in
Chapter 14. We would like to thank the School of Economics at The University of Queensland for the opportunity to teach benefit-cost analysis in a diverse and stimulating
environment. We have enjoyed excellent support from all members of the School’s administrative staff in the preparation of the manuscript and, in particular from Gloria Barr who has
incorporated our frequent revisions with patience and efficiency. We received helpful
comments on earlier drafts from several anonymous reviewers, and from Dale Squires. We
would like to thank these people for their suggestions and to absolve them from any responsibility for any remaining errors.

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